Our comprehensive Data Science Research program is organized into 4 complementary Algorithm Research Cores: (1) Imaging Genomics, (2) Connectomics, (3) Machine Learning & Clinical Prediction, and (4) ENIGMA Disease Working Groups. World leaders in each field lead each Core, tackling computational questions on a scale not previously imagined or attempted. BigData tools will fuel ENIGMA'S worldwide scientific discoveries. We combine innovations in mathematics, machine learning, genomics, consortium science, and expertise from >20 countries and >125 institutions. ENIGMA is not a project, it is a scientific movement of rapidly and constantly Interacting collaborations that support each other. ENIGMA cohorts boost each other's power with gigantic datasets, tools and expertise to maximally exploit each other's data, performing some of the world's largest disease studies, beyond what any one site could perform alone. ENIGMA is distributed computation at its best, drawing on gigantic datasets and expertise. We create massive economic savings - drawing on worldwide computational and infrastructural resources vastly beyond what any one site in any one country would apply to a targeted biomedical goal. We bring BigData Science and the ENIGMA Consortium together to advance Worldwide Medicine. In Cores 1 and 2 we mine images and connectomes for genetic markers that re-wire the brain or boost brain tissue loss, using new mathematics to prioritize and organize trillions of computations, jointly searching images and genomes. In Core 3, we unleash multi-task sparse learning to predict diagnosis and prognosis from vast high-dimensional biomarker data in the largest neuroimaging genetics datasets ever. In Core 4 we use these tools in a massive distributed computation: a vast, mutually interacting set of 9 Worldwide Working Groups, led by experts in 9 major diseases of the brain - schizophrenia, bipolar, major depression, ADHD, autism, OCD, 22q deletion syndrome, HIV/AIDS, and addictions. We will discover what genes, medications, and lifestyle factors promote or resist brain disease worldwide. Our ENIGMA Center is a worldwide movement in mutually supportive discovery in medicine - spurred on by tools to perform gigantic computations never before Imagined.